AAWSAP DIRD, Quantum Tomography of Negative Energy States in the Vacuum, January 2011

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Quantum Tomography of Negative Energy States in the
Vacuum
Introduction
Future aerospace vehicles could have an advanced propulsion system that uses
negative quantum vacuum energy to modify the spacetime geometry in the immediate
vicinity surrounding the vehicle in order to induce faster-than-light motion via
traversable wormholes or warp drives, or even levitation via antigravity [1, 2]. These
exotic propulsion concepts are well-known in mainstream general relativity and
quantum field theory research. The notion of a physical state with negative energy is
not familiar in the realm of classical physics. However, it is not rare in quantum field
theory to have quantum states with negative energy density or a negative energy flux.
Even for a quantum scalar field in the flat Minkowski spacetime, it can be proved that
the existence of quantum states with negative energy density is inevitable [3].
Although all known forms of classical matter have non-negative energy density, it is not
so in quantum field theory. A general quantum state can be a superposition of particle
number eigenstates and may have a negative expectation value of energy density in
certain spacetime regions due to quantum coherence effects [3]. These considerations
remain true even for quantum fields in a curved spacetime where the effects of
gravitational fields, or equivalently, accelerations, can be observed due to the mass of
astronomical bodies or the motions of astronomical bodies.
There are two key examples of specially prepared quantum vacuum states that are
known to produce small amounts of negative energy density in the laboratory. These
are the well-known Casimir effect and the squeezed vacuum states of the
electromagnetic field. The former is a static quantum vacuum effect wh ile the latter is
a time-domain quantum vacuum effect. There are several other examples of special
quantum vacuum or particle states that produce negative energy density, but they are
beyond the scope of this report because they remain mathematical curiosities or are not
practicable to im plement in the laboratory in the foreseeable future.
We already make small amounts of negative energy in the laboratory via the Casimir
effect and squeezed electromagnetic vacuum states, but we do not yet know if we can
access larger amounts for extended periods of time over extended spatial distributions
for the purpose of modifying spacetime for aerospace propulsion applications. It will be
necessary to first explore the quantum nature of the Casimir effect and squeezed
electromagnetic vacuum states to determine whether we can measure and spatially
map their negative energy density. This is a necessary first step to take before
beginning any study on producing large quantities of negative energy because we will
first need to know how to measure and spatially map negative energy in order to
properly control it after producing it. This is the motivation for this report.
We need to firm up our understanding of how lab detectors will respond to negative
energy in situ. A first step in this direction was already taken by Hansen et al. [4] in
2001 for the time-domain negative energy pulses in squeezed electromagnetic vacuum
states, and more recently Marecki [5, 6] generalized the analysis of the output of
balanced homodyne detectors (BHDs) for the case of static negative energy states
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